Optical and Quantum Electronics

, Volume 35, Issue 4–5, pp 381–394

Three-dimensional vectorial analysis of waveguide structures with the method of lines



The method of lines (MoL) a special eigenmode algorithm has been proven as an efficient tool for the analysis of waveguide structures in optics and microwaves. The electric and magnetic fields in the cross-section and their derivatives with respect to the cross-section coordinates are discretized with finite differences (FD) while analytic expressions are used in the direction of propagation. The numerical effort for analyzing three-dimensional structures with a two-dimensional discretization can be very high, particularly if vectorial characteristics have to be taken into account. In this paper we introduce a reduction of the eigenmode system to keep the effort moderate. Only a certain number of eigenmodes is determined with the Arnoldi algorithm. We will show then how the electric field distribution of the eigenmodes can be computed from the magnetic field and vice versa. To match the fields at the interfaces we introduce left eigenvectors which are the inverse of the field distributions. The formulas were applied to the analysis of a polarization converter consisting of a periodical perturbation of a waveguide structure. A rotation angle greater than 80° was determined.

eigenmode reduction method of lines polarization converters 


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  1. Ando, T., T. Murata, H. Nakayama, J. Yamauchi and H. Nakano. IEEE Photon. Technol. Lett. 14 1288, 2002.Google Scholar
  2. Felsen, L.B. and N. Marcuvitz (eds.) Radiation and Scattering of Waves. IEEE Press, New York, USA, 1996.Google Scholar
  3. Gerdes, J. Electron. Lett. 30 550, 1994.Google Scholar
  4. Gerdes, J., S. Helfert and R. Pregla. Electron. Lett. 31 65, 1995.Google Scholar
  5. Golub, G.H. and C.F. van Loan. Matrix computations, p. 501. Johns Hopkins University Press, Baltimore, USA, 1989.Google Scholar
  6. Grossard, N., H. Forte, J.P. Vilcot, B. Beche and J.P. Goedgebuer. IEEE Photon. Technol. Lett. 13 830, 2001.Google Scholar
  7. Helfert, S.F. and R. Pregla. J. Lightwave Technol. 16 1694, 1998.Google Scholar
  8. Helfert, S.F. and R. Pregla. Electromagnetics. Invited paper for the special issue on 'Optical wave propagation in guiding structures' 22 615, 2002.Google Scholar
  9. Koster, T. and P.V. Lambeck. J. Lightwave Technol. 19 876, 2001.Google Scholar
  10. Mustieles, F.J., E. Ballesteros and F. Hernández-Gil. IEEE Photon. Technol. Lett. 5 809, 1993.Google Scholar
  11. Obayya, A.S.S., B.M. Azizur-Rahman, K.T.V. Grattan and H.A. Ei-Mikati. Appl. Opt. 40 5395, 2001.Google Scholar
  12. Pregla, R. In Methods for Modeling and Simulation of Guided-Wave Optoelectronic Devices (PIER 11), Progress in Electromagnetic Research, (ed.) W.P. Huang, p. 51. EMW Publishing, Cambridge, Massachusetts, USA, 1995.Google Scholar
  13. Pregla, R. AEÜ 50 293, 1996.Google Scholar
  14. Pregla, R. In: Integr. Photo. Resear. Technic. Digest., p. 40. Santa Barbara, USA, 1999a.Google Scholar
  15. Pregla, R. In: European Conference on IntegratedOptics and Technical Exhibit., p. 55. Torino, Italy, 1999b.Google Scholar
  16. Pregla, R. In: U.R.S.I Intern. Symp. Electromagn. Theo., p. 425. Victoria, Canada, 2001.Google Scholar
  17. Pregla, R. IEEE Trans. Microw. Theory Tech. 50 1469, 2002.Google Scholar
  18. Pregla, R. and W. Pascher. In Numerical Techniques for Microwave andMillimeter Wave Passive Structures, (ed.) T. Itoh, p. 381. J. Wiley Publ., New York, USA, 1989.Google Scholar
  19. Rogge, U. and R. Pregla. J. Lightwave Technol. 11 2015, 1993.Google Scholar
  20. Schneider, V.M. Opt. Commun. 160 230, 1999.Google Scholar
  21. Strang, G. Linear Algebra andits Applications, 3rd edn. p. 130. Saunders HBJ College Publishers, Orlando, FL, USA, 1986.Google Scholar

Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  1. 1.FernUniversität, D-HagenGermany

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